(Reuters) - Despite sharp criticism from U.S. President Donald Trump for raising interest rates, Federal Reserve policymakers remain generally united on the need to raise borrowing costs further, according to minutes from their most recent policy meeting.

Every policymaker backed the Fed's September rate increase, according to the minutes of the Sept. 25-26 meeting, published Wednesday. The display of unanimity could bolster expectations the central bank will raise rates a fourth time this year in December.

Participants in the FOMC rate-setting committee "generally anticipated that further gradual increases" in short-term borrowing costs would be consistent with the kind of continued economic expansion, labour market strength, and firm inflation that most anticipated, the minutes showed.

"This gradual approach would balance the risk of tightening monetary policy too quickly, which could lead to an abrupt slowing in the economy and inflation moving below the Committee’s objective, against the risk of moving too slowly, which could engender inflation persistently above the objective and possibly contribute to a buildup of financial imbalances," the minutes said.

U.S. stock prices recovered some earlier losses but were still down for the day following the minutes. U.S. Treasury yields were little changed. Trump has accused the Fed of endangering the country's economic health, this week saying the central bank is his "biggest threat" and last week calling the central bank "crazy," "loco," "ridiculous," and "too cute."

Though the minutes did not refer to any of Trump's criticism, its message of further rate increases suggests that policymakers are not fazed by it.

"For now, the Fed has made it clear that they are focused on their agenda despite rising Presidential pressure on their rate decisions," said Mike Loewengart, vice president of investment strategy at E*Trade.

The minutes did suggest that the committee remains split on how much further to raise rates next year, with a few participants expecting rates would need to rise enough to modestly restrain economic growth, even as two others "indicated that they would not favour adopting a restrictive policy stance in the absence of clear signs of an overheating economy and rising inflation."

Compared to the minutes of Fed's previous meeting held in August, the September minutes appeared to show less discussion around the prospects that a recession might be lurking around the corner. Rather, some of the central bankers appeared to see some indications of a stronger U.S. economy.

"Almost all participants saw little change in their assessment of the economic outlook, although a few of them judged that recent data pointed to a pace of economic activity that was stronger than they expected earlier in the year," according to the minutes.

Still, policymakers noted that the relative weakness of the international economy could create "potential for further strengthening of the U.S. dollar," a factor that could weigh on U.S. exports.

They also noted that some businesses said they were investing less in the energy sector due to the imposition of import tariffs on steel and aluminium, part of an array of trade policy conflicts the Trump administration has pursued.

The U.S. economy has been growing more quickly this year than many economists believe is possible without generating higher inflation, with the jobless rate at its lowest level in decades.

The Fed has been raising interest rates since 2015 and after the rate hike last month it stopped describing the stance of monetary policy as "accommodative," meaning that it no longer thought the level of interest rates was stimulating the economy.

The minutes showed that "almost all" policymakers agreed it was time to stop saying they were stimulating the economy.